Question

Q 4

Answer 1

Required sum = `2/5+3/5^2+2/5^3+3/5^4+2/5^5+3/5^6+...............`

`=(2/5+2/5^3+2/5^5+........)+(3/5^2+3/5^4+3/5^6+........)`

`=2/5(1+1/5^2+1/5^4+........)+3/5^2(1+1/5^2+1/5^4+........)`

`=2/5[1/(1-1/25)]+3/25[1/(1-1/25)]`

`=2/5xx25/24+3/25xx25/24`

`=5/12+1/8`

`=(10+3)/24`

`=13/24`